The radius of `La^(3+)(Z=57)` is 106 pm. Which one of the following given values will be closest to the radius of `Lu^(3+)(Z=71)`?

Options

A. 160 pm
B. 140 pm
C. 106 pm
D. 85 pm

Explanation

To find the radius of `Lu^(3+)` (Lutetium ion) based on the given radius of `La^(3+)` (Lanthanum ion), we can follow these steps:

### Step 1: Understand the trend in ionic radii
The ionic radii of lanthanides generally decrease as we move from La to Lu. This is due to the increasing nuclear charge, which pulls the electrons closer to the nucleus, resulting in a smaller ionic radius.

**Hint:** Remember that as you move across a period or a series in the periodic table, the ionic radius typically decreases due to increased nuclear charge.

### Step 2: Compare the ionic radii of La and Lu
Given that the radius of `La^(3+)` is 106 pm, we need to determine that `Lu^(3+)` will have a smaller radius. Since Lutetium is the last element in the lanthanide series, its ionic radius will be less than that of Lanthanum.

**Hint:** Consider that the trend in ionic radii for lanthanides is a gradual decrease from La to Lu.

### Step 3: Eliminate options based on size
Since we know that the radius of `Lu^(3+)` must be less than 106 pm, we can eliminate any options that are equal to or greater than 106 pm.

**Hint:** Look for values that are less than 106 pm to find the closest approximation for `Lu^(3+)`.

### Step 4: Identify the closest value
After eliminating the options that are not valid, we should be left with one or more values that are less than 106 pm. Among these, we need to select the one that is numerically closest to 106 pm.

**Hint:** Compare the remaining options to see which one is nearest to 106 pm.

### Conclusion
Based on the trend and the elimination of options, the closest value to the radius of `Lu^(3+)` is the one that is less than 106 pm and closest in numerical value.

**Final Answer:** The correct answer is option D (assuming option D is less than 106 pm and is the closest value).